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JOURNALS // Vestnik Tomskogo Gosudarstvennogo Universiteta. Matematika i Mekhanika // Archive

Vestn. Tomsk. Gos. Univ. Mat. Mekh., 2025 Number 97, Pages 66–82 (Mi vtgu1190)

MECHANICS

Numerical study of the mechanical behavior of a spinal segment with osteosarcoma under physiological and acoustic loading

G. M. Ereminaa, A. Yu. Smolinba, I. P. Martyshinaa

a Institute of Strength Physics and Materials Science of the Siberian Branch of the Russian Academy of Sciences, Tomsk, Russian Federation
b Tomsk State University, Tomsk, Russian Federation

Abstract: Determination of the stress state is a key aspect in developing methods for the mechanical stimulation of structural reorganization processes in biological tissues. The most important features of human skeletal materials include permeability, porosity (varying in a wide range of values and saturated with biological fluid), and a broad spectrum of elastic properties. Neoplastic processes in the bone matrix lead to local structural reorganization of the tissue in the affected area, which is characterized by reduced elastic characteristics and permeability.
A macromechanical model of the fourth and fifth thoracic vertebrae segments is developed with allowance for realistic poroelastic parameters of biological tissues, including tumor formation. To describe the mechanical behavior of biological tissues, the modified Biot model of poroelasticity is used and adapted to the method of movable cellular automata. A geometric model of the thoracic spine segment is constructed in FreeCAD, accounting for its structural features. The model is studied under loads similar to physiological conditions and under external acoustic exposure.
Analysis of the simulation results based on mechanobiological principles shows that under physiological loading, the levels of hydrostatic and pore fluid pressures are insufficient to suppress the differentiation and proliferation of cancer cells. Under acoustic exposure with an intensity of 0.2-0.3 mJ/mm$^2$ in the area with neoplastic process, the conditions are provided for transferring healthy stem cells and regeneration of bone tissue in the affected area.

Keywords: stress-strain state, poroelastic model, method of movable cellular automata, biological tissues, cancer.

UDC: 539.32

Received: 04.12.2024
Accepted: September 6, 2025

DOI: 10.17223/19988621/97/5



© Steklov Math. Inst. of RAS, 2026